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on Econometric Time Series |
| By: | Tobias Hartl; Roland Weigand |
| Abstract: | We propose convenient inferential methods for potentially nonstationary multivariate unobserved components models with fractional integration and cointegration. Based on finite-order ARMA approximations in the state space representation, maximum likelihood estimation can make use of the EM algorithm and related techniques. The approximation outperforms the frequently used autoregressive or moving average truncation, both in terms of computational costs and with respect to approximation quality. Monte Carlo simulations reveal good estimation properties of the proposed methods for processes of different complexity and dimension. |
| Date: | 2018–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1812.09142&r=all |
| By: | Delle Monache, Davide (Bank of Italy); Petrella, Ivan (University of Warwick and CEPR) |
| Abstract: | In this work we explore a novel approach to estimating Gaussian state space models in the classical framework without making use of the Kalman filter and Kalman smoother. By formulating the model in matrix form, we obtain expressions for the likelihood function and the smoothed state vector that are computationally feasible and generally more efficient than the standard filtering approach. Finally, we highlight a convenient way to retrieve the filtering weights and to deal with data irregularities. |
| Keywords: | State space models; Likelihood; Smoother; Sparse matrices; JEL Classification Numbers: C22 ; C32 ; C51 ; C53; C82; |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:wrkemf:19&r=all |
| By: | Hauzenberger, Niko; Huber, Florian |
| Abstract: | In this paper we aim to improve existing empirical exchange rate models by accounting for uncertainty with respect to the underlying structural representation. Within a flexible Bayesian non-linear time series framework, our modeling approach assumes that different regimes are characterized by commonly used structural exchange rate models, with their evolution being driven by a Markov process. We assume a time-varying transition probability matrix with transition probabilities depending on a measure of the monetary policy stance of the central bank at the home and foreign country. We apply this model to a set of eight exchange rates against the US dollar. In a forecasting exercise, we show that model evidence varies over time and a model approach that takes this empirical evidence seriously yields improvements in accuracy of density forecasts for most currency pairs considered. |
| Keywords: | Empirical exchange rate models, exchange rate fundamentals, Markov switching |
| Date: | 2018–12 |
| URL: | http://d.repec.org/n?u=RePEc:wiw:wus005:6770&r=all |
| By: | Tobias Hartl; Roland Weigand |
| Abstract: | We investigate a setup for fractionally cointegrated time series which is formulated in terms of latent integrated and short-memory components. It accommodates nonstationary processes with different fractional orders and cointegration of different strengths and is applicable in high-dimensional settings. In an application to realized covariance matrices, we find that orthogonal short- and long-memory components provide a reasonable fit and competitive out-of-sample performance compared to several competitor methods. |
| Date: | 2018–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1812.09149&r=all |
| By: | Davy Paindaveine; Julien Remy; Thomas Verdebout |
| Abstract: | We consider inference on the first principal direction of a p -variate elliptical distribution. We do so in challenging double asymptotic scenarios for which this direction eventually fails to be identifiable. In order to achieve robustness not only with respect to such weak identifiability but also with respect to heavy tails, we focus on sign-based statistical procedures, that is, on procedures that involve the observations only through their direction from the center of the distribution. We actually consider the generic problem of testing the null hypothesis that the first principal direction coincides with a given direction of R p. We first focus on weak identifiability setups involving single spikes (that is, involving spectra for which the smallest eigenvalue has multiplicity p-1). We show that, irrespective of the degree of weak identifiability, such setups offer local alternatives for which the corresponding sequence of statistical experiments converges in the Le Cam sense. Interestingly, the limiting experiments depend on the degree of weak identifiability. We exploit this convergence result to build optimal sign tests for the problem considered. In classical asymptotic scenarios where the spectrum is fixed, these tests are shown to be asymptotically equivalent to the sign-based likelihood ratio tests available in the literature. Unlike the latter, however, the proposed sign tests are robust to arbitrarily weak identifiability. We show that our tests meet the asymptotic level constraint irrespective of the structure of the spectrum, hence also in possibly multi-spike setups. Finally, we fully characterize the non-nullasymptotic distributions of the corresponding test statistics under weak identifiability, which allows us to quantify the corresponding local asymptotic powers. Monte Carlo exercises confirm our asymptotic results. |
| Keywords: | Le Cam's asymptotic theory of statistical experiments, Local asymptotic normality, Principal component analysis, Sign tests, Weak identi ability. |
| Date: | 2019–01 |
| URL: | http://d.repec.org/n?u=RePEc:eca:wpaper:2013/280742&r=all |
| By: | Corrado, L.; Stengos, T.; Weeks, M.; Ege Yazgan, M. |
| Abstract: | In many applications common in testing for convergence the number of cross-sectional units is large and the number of time periods are few. In these situations asymptotic tests based on an omnibus null hypothesis are characterised by a number of problems. In this paper we propose a multiple pairwise comparisons method based on an a recursive bootstrap to test for convergence with no prior information on the composition of convergence clubs. Monte Carlo simulations suggest that our bootstrap-based test performs well to correctly identify convergence clubs when compared with other similar tests that rely on asymptotic arguments. Across a potentially large number of regions, using both cross-country and regional data for the European Union we find that the size distortion which afflicts standard tests and results in a bias towards finnding less convergence, is ameliorated when we utilise our bootstrap test. |
| Keywords: | Multivariate stationarity, bootstrap tests, regional convergence. |
| JEL: | C51 R11 R15 |
| Date: | 2018–12–21 |
| URL: | http://d.repec.org/n?u=RePEc:cam:camdae:1873&r=all |
| By: | Gabriele Fiorentini (Università di Firenze, Italy; Rimini Centre for Economic Analysis); Enrique Sentana (CEMFI, Spain) |
| Abstract: | We propose tests for smooth but persistent serial correlation in risk premia and volatilities that exploit the non-normality of financial returns. Our parametric tests are robust to distributional misspecification, while our semiparametric tests are as powerful as if we knew the true return distribution. Local power analyses confirm their gains over existing methods, while Monte Carlo exercises assess their finite sample reliability. We apply our tests to quarterly returns on the five Fama-French factors for international stocks, whose distributions are mostly symmetric and fat-tailed. Our results highlight noticeable differences across regions and factors and confirm the fragility of Gaussian tests. |
| Keywords: | financial forecasting, moment tests, misspecification, robustness, volatility |
| JEL: | C12 C22 G17 |
| Date: | 2019–01 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:19-01&r=all |
| By: | Pavel Ciaian; d'Artis Kancs; Miroslava Rajcaniova |
| Abstract: | This is the first paper that estimates the price determinants of BitCoin in a Generalised Autoregressive Conditional Heteroscedasticity framework using high frequency data. Derived from a theoretical model, we estimate BitCoin transaction demand and speculative demand equations in a GARCH framework using hourly data for the period 2013-2018. In line with the theoretical model, our empirical results confirm that both the BitCoin transaction demand and speculative demand have a statistically significant impact on the BitCoin price formation. The BitCoin price responds negatively to the BitCoin velocity, whereas positive shocks to the BitCoin stock, interest rate and the size of the BitCoin economy exercise an upward pressure on the BitCoin price. |
| Date: | 2018–12 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1812.09452&r=all |
| By: | Shaw, Charles |
| Abstract: | In a recent contribution to the financial econometrics literature, Chu et al. (2017) provide the first examination of the time-series price behaviour of the most popular cryptocurrencies. However, insufficient attention was paid to correctly diagnosing the distribution of GARCH innovations. When these data issues are controlled for, their results lack robustness and may lead to either underestimation or overestimation of future risks. The main aim of this paper therefore is to provide an improved econometric specification. Particular attention is paid to correctly diagnosing the distribution of GARCH innovations by means of Kolmogorov type non-parametric tests and Khmaladze's martingale transformation. Numerical computation is carried out by implementing a Gauss-Kronrod quadrature. Parameters of GARCH models are estimated using maximum likelihood. For calculating P-values, the parametric bootstrap method is used. Further reference is made to the merits and demerits of statistical techniques presented in the related and recently published literature. |
| Keywords: | Autoregressive conditional heteroskedasticity (ARCH), generalized autoregressive conditional heteroskedasticity (GARCH), market volatility, nonlinear time series, Khmaladze transform. |
| JEL: | C22 C58 |
| Date: | 2018–11–01 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:90437&r=all |
| By: | Aknouche, Abdelhakim; Demmouche, Nacer; Touche, Nassim |
| Abstract: | A Bayesian MCMC estimate of a periodic asymmetric power GARCH (PAP-GARCH) model whose coefficients, power, and innovation distribution are periodic over time is proposed. The properties of the PAP-GARCH model such as periodic ergodicity, finiteness of moments and tail behaviors of the marginal distributions are first examined. Then, a Bayesian MCMC estimate based on Griddy-Gibbs sampling is proposed when the distribution of the innovation of the model is standard Gaussian or standardized Student with a periodic degree of freedom. Selecting the orders and the period of the PAP-GARCH model is carried out via the Deviance Information Criterion (DIC). The performance of the proposed Griddy-Gibbs estimate is evaluated through simulated and real data. In particular, applications to Bayesian volatility forecasting and Value-at-Risk estimation for daily returns on the S&P500 index are considered. |
| Keywords: | Periodic Asymmetric Power GARCH model, probability properties, Griddy-Gibbs estimate, Deviance Information Criterion, Bayesian forecasting, Value at Risk. |
| JEL: | C11 C15 C58 |
| Date: | 2018–05–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:91136&r=all |
| By: | Dominik Bertsche (Department of Economics, Box 129, 78457 Konstanz, Germany); Ralf Brüggemann (Department of Economics, Box 129, 78457 Konstanz, Germany); Christian Kascha |
| Abstract: | We represent the dynamic relation among variables in vector autoregressive (VAR) models as directed graphs. Based on these graphs, we identify so-called strongly connected components (SCCs). Using this graphical representation, we consider the problem of variable selection. We use the relations among the strongly connected components to select variables that need to be included in a VAR if interest is in forecasting or impulse response analysis of a given set of variables. We show that the set of selected variables from the graphical method coincides with the set of variables that is multi-step causal for the variables of interest by relating the paths in the graph to the coecients of the `direct' VAR representation. Empirical applications illustrate the usefulness of the suggested approach: Including the selected variables into a small US monetary VAR is useful for impulse response analysis as it avoids the well-known `price-puzzle'. We also nd that including the selected variables into VARs typically improves forecasting accuracy at short horizons. |
| Keywords: | Vector autoregression, Variable selection, Directed graphs, Multi-step causal-ity, Forecasting, Impulse response analysis |
| JEL: | C32 C51 E52 |
| Date: | 2018–12–10 |
| URL: | http://d.repec.org/n?u=RePEc:knz:dpteco:1808&r=all |
| By: | Gergely Ganics (Banco de España); Atsushi Inoue (Vanderbilt University); Barbara Rossi (ICREA - Univ. Pompeu Fabra) |
| Abstract: | In this paper we propose methods to construct confidence intervals for the bias of the two-stage least squares estimator, and the size distortion of the associated Wald test in instrumental variables models. Importantly our framework covers the local projections — instrumental variable model as well. Unlike tests for weak instruments, whose distributions are non-standard and depend on nuisance parameters that cannot be estimated consistently, the confidence intervals for the strength of identification are straightforward and computationally easy to calculate, as they are obtained from inverting a chi-squared distribution. Furthermore, they provide more information to researchers on instrument strength than the binary decision offered by tests. Monte Carlo simulations show that the confidence intervals have good small sample coverage. We illustrate the usefulness of the proposed methods to measure the strength of identification in two empirical situations: the estimation of the intertemporal elasticity of substitution in a linearized Euler equation, and government spending multipliers. |
| Keywords: | instrumental variables, weak instruments, weak identification, concentration parameter, local projections |
| JEL: | C22 C52 C53 |
| Date: | 2018–12 |
| URL: | http://d.repec.org/n?u=RePEc:bde:wpaper:1841&r=all |
| By: | Chen, Siyan; Desiderio, Saul |
| Abstract: | In this paper we present a simple approach to factor analysis to estimate the true correlations between observable variables and a single common factor. We first provide the exact formula for the correlations under the orthogonality conditions, and then we show how to consistently estimate them using a random sample and a proper instrumental variable. |
| Keywords: | Factor analysis, correlation, instrumental variable estimation |
| JEL: | C1 C38 |
| Date: | 2018 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:90426&r=all |